Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 1/(x-3)^2-3/(x-3)-4=0
-
Equation x^4+2*x^2-8=0
-
Equation (x-2)^5+(4-x)^5=2
-
Equation 6/(x+5)=-5
- Express {x} in terms of y where:
- 17*x-20*y=6
- 5*x-13*y=17
- 6*x+17*y=3
- 1*x+4*y=20
-
Identical expressions
- sqrt2*cos(x)- one = zero
- square root of 2 multiply by co sinus of e of (x) minus 1 equally 0
- square root of 2 multiply by co sinus of e of (x) minus one equally zero
- √2*cos(x)-1=0
- sqrt2cos(x)-1=0
- sqrt2cosx-1=0
- sqrt2*cos(x)-1=O
-
Similar expressions
- (sinx-sin2x)/sqrt(2cosx-1)=0
- sqrt2*cos(x)+1=0
- sqrt2*cosx-1=0
sqrt2*cos(x)-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{2} \cos{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
We get:
$$\sqrt{2} \cos{\left(x \right)} = 1$$
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
$$\sqrt{2} \cos{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
Move -1 to right part of the equation
with the change of sign in -1
We get:
$$\sqrt{2} \cos{\left(x \right)} = 1$$
Divide both parts of the equation by sqrt(2)
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Rapid solution
[src]
pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
7*pi
x2 = ----
4
$$x_{2} = \frac{7 \pi}{4}$$
x2 = 7*pi/4
Sum and product of roots
[src]
sum
pi 7*pi -- + ---- 4 4
$$\frac{\pi}{4} + \frac{7 \pi}{4}$$
=
2*pi
$$2 \pi$$
product
pi 7*pi --*---- 4 4
$$\frac{\pi}{4} \frac{7 \pi}{4}$$
=
2 7*pi ----- 16
$$\frac{7 \pi^{2}}{16}$$
7*pi^2/16
Numerical answer
[src]
x1 = -101.316363078271
x2 = 93.4623814442964
x3 = 43.1968989868597
x4 = -55.7632696012188
x5 = -19.6349540849362
x6 = 13.3517687777566
x7 = -44.7676953136546
x8 = 95.0331777710912
x9 = 11.7809724509617
x10 = 32.2013246992954
x11 = 9111.4040935738
x12 = 18.0641577581413
x13 = 25.9181393921158
x14 = 51.0508806208341
x15 = 74.6128255227576
x16 = 63.6172512351933
x17 = -57.3340659280137
x18 = 88.7499924639117
x19 = -76.1836218495525
x20 = -32.2013246992954
x21 = -99.7455667514759
x22 = -18.0641577581413
x23 = 30.6305283725005
x24 = -82.4668071567321
x25 = -38.484510006475
x26 = -351.072979038659
x27 = 82.4668071567321
x28 = 38.484510006475
x29 = -62.0464549083984
x30 = 49680.3608257056
x31 = -36.9137136796801
x32 = 68.329640215578
x33 = -13.3517687777566
x34 = -88.7499924639117
x35 = 76.1836218495525
x36 = 80.8960108299372
x37 = -51.0508806208341
x38 = -11.7809724509617
x39 = -182.997772071605
x40 = 7.06858347057703
x41 = -68.329640215578
x42 = 57.3340659280137
x43 = 0.785398163397448
x44 = -24.3473430653209
x45 = 36.9137136796801
x46 = -74.6128255227576
x47 = -162.577419823272
x48 = -69.9004365423729
x49 = -7.06858347057703
x50 = 19.6349540849362
x51 = 49.4800842940392
x52 = 62.0464549083984
x53 = 69.9004365423729
x54 = -25.9181393921158
x55 = 44.7676953136546
x56 = -30.6305283725005
x57 = 87.1791961371168
x58 = -0.785398163397448
x59 = 24.3473430653209
x60 = -49.4800842940392
x61 = 5.49778714378214
x62 = -5.49778714378214
x63 = -43.1968989868597
x64 = -63.6172512351933
x65 = 99.7455667514759
x66 = -80.8960108299372
x67 = 55.7632696012188
x68 = -93.4623814442964
x69 = -95.0331777710912
x70 = -87.1791961371168
x70 = -87.1791961371168